Factor & Remainder Theorem

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³ - 5x² + 2x - 10

• 0
• 2x-10
• -2x-10
• 2x+10

Tags

CCSS.HSA.APR.B.2

Is (x-3) a factor of
(x³ - 3x² + 2x + 2)?

• Yes
• No

Tags

CCSS.HSA.APR.B.2

Is (x-7) a factor of (x²-5x+14)?

• Yes
• No

Tags

CCSS.HSA.APR.B.2

Find all the factors of   x³ -3x² -4x +12 given that -2 is a zero.

• (x-2) (x+2) (x+3) 
• (x-2) (x-2) (x+3)
• (x+2) (x+2) (x+3)
• (x-2) (x+2) (x-3)

Tags

CCSS.HSA.APR.B.2

What is the remainder when a³ - 4 is divided by a+2? 

• -2
• -6
• -12
• 0

Tags

CCSS.HSA.APR.B.2

Find all the zeros, given that f(-3) = 0
f(x) = 2x³+5x²-6x-9

• -1,-3,-3
• -1,-3,3/2
• 3,3,3
• -3,2/3,-1

Tags

CCSS.HSF-IF.C.7C

Find all the real zeros of the function 
f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

• x = 1/2, -6
• x = -1/2, 6
• x = 4, -1/2, 6
• x = -4, 1/2, -6

Tags

CCSS.HSA.APR.B.2

What is the remainder of  (3x³ -5x² -4x +1) ÷ (x + 3)?

• -25
• 25
• 113
• -113

Tags

CCSS.HSA.APR.B.2

What are the three factors for
 (x³ +7x² +7x -15) ÷ (x -1)?

• (x-1) (x+5) (x-3) 
• (x-1) (x+5) (x + 3) 
• (x+1) (x+5) (x-3) 
• (x+1) (x-5) (x-3) 

Tags

CCSS.HSA.APR.B.2